the orbit does not change with time. However, the electron will move from a lower stationary state to a higher stationary state when required amount of energy is absorbed by the electron or energy is emitted when electron moves from higher stationary state to lower stationary state (equation . ). The energy change does not take place in a continuous manner.
Angular Momentum Just as linear momentum is the product of mass ( m ) and linear velocity (v), angular momentum is the product of moment of inertia ( I ) and angular velocity ( ω ). For an electron of mass m e , moving in a circular path of radius r around the nucleus, angular momentum = I × ω Since I = m e r , and ω = v/ r where v is the linear velocity, ∴ angular momentum = m e r × v/ r = m e v r iii) The frequency of radiation absorbed or emitted when transition occurs between two stationary states that differ in energy by ∆ E , is given by: ( . ) Where E and E are the energies of the lower and higher allowed energy states respectively. This expression is commonly known as Bohr’s frequency rule.
iv) The angular momentum of an electron is quantised. In a given stationary state it can be expressed as in equation ( . ) m r n h e v . n = , , .....
( . ) Where m e is the mass of electron, v is the velocity and r is the radius of the orbit in which electron is moving. Thus an electron can move only in those orbits for which its angular momentum is integral multiple of h / π. That means angular momentum is quantised.
Radiation is emitted or obsorbed only when transition of electron takes place from one quantised value of angular momentum to another. Therefore, Maxwell’s electromagnetic theory does not apply here that is why only certain fixed orbits are allowed. The details regarding the derivation of energies of the stationary states used by